带线性项Kirchhoff型问题的无穷多古典解  

Infinitely Many Classical Solutions for Kirchhoff Type Problem with Linear Term

作　　者：王跃 叶红艳 雷俊 索洪敏 WANG Yue;YE Hongyan;LEI Jun;SUO Hongmin(School of Mathematics and Statistics,Guizhou University,Guiyang Guizhou 550025,China;School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang Guizhou 550025,China)

机构地区：[1]贵州大学数学与统计学院,贵州贵阳550025 [2]贵州民族大学数据科学与信息工程学院,贵州贵阳550025

出　　处：《广西师范大学学报（自然科学版）》2020年第6期65-73,共9页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11661021,11861021);贵州教育厅科研基金(黔教合KY字[2016]029号,黔教合KY字[2016]163号);贵州科技厅科研基金(黔科合基础[2019]1163号)。

摘　　要：在Neumann边界条件下研究一类带线性指数的非局部Kirchhoff型问题,利用特殊函数构造和分部讨论的方法,获得了无穷多古典解{un}∞n=1的存在性,并且n→∞时un→0。在变分意义下,这些解所对应变分泛函的能量值收敛到非零常数。另外,该问题近共振解所对应的泛函能量值收敛到零。这些结论对Dirichlet边界条件也成立。Nonlocal Kirchhoff type problem with linear exponent on Neumann’s boundary condition are considered in this paper.Infinitely many classical solutions{un}∞n=1 are obtained by using constructors of special functions and partial discussion,where un→0 as n→+∞.In terms of variation methods,for those solutions,the energies of corresponding functional are converged to a nonzero constant.Moreover the energies of corresponding functional are converged to zero for the solutions near resonances in this problem.All results mentioned above are suitable for Dirichlet’s boundary condition.

关 键 词：无穷多古典解 线性指数 函数构造 非局部问题 近共振 

分 类 号：O175.23[理学—数学]